In this chapter, we examine a number of issues in calculating the benefits of prudential policy. We first look at the crisis model and examine a number of variables that better predict the probability that a financial crisis occurs. We also examine a number of alternative specifications for the model. We find that the probability of crisis is dependent on the calibration of capital and liquidity policy, as well as both domestic and external economic conditions. A further issue addressed is the calculation of benefits. Our model of the banking system shows that banks respond to changes in prudential policy over time. As our crisis model only calculates the probability that a crisis occurs within a given year, we need to consider a Bernoulli process to calculate the reduction in the probability of crisis (and hence the benefits) over a comparable period to that used to calculate the costs. Finally, we look at the losses to the economy when a financial crisis occurs, which may have either permanent or transient impacts on the economy. Financial crises that have a permanent effect on economic output impose much greater losses on the economy. If crises with permanent effects become less frequent in future as a result of tighter prudential policy, the losses avoided (and hence the measured benefits) will also be higher.
As noted in Section 2.1, our approach to the benefits of prudential standards is based on OP38, which models the probability of a banking crisis (the crisis model). The early warning literature underpins modelling of the probability of a banking crisis in OP38 and the authors discuss in detail the literature on macroeconomic early warning systems. We stress here that models derived from this literature allow us to estimate the probability of bank crises using factors likely to signal a crisis, but the models do not imply causal relationships. The chosen specification in OP38 is derived by using model selection techniques on a large set of regressors in a logit specification of a zero-one indicator of crisis occurrence. The data are for all banking crises (whether or not these crises had broader, permanent economic consequences or not) and cover a panel of OECD countries between 1980 and 2008. The banking crisis variable is consistent with the definitions set out in OP38 and
Barrell et al. (2010a).12 The model includes the capital ratio in the banking
sector (LEV), the broad liquidity ratio in the banking sector (LIQ) and the
lagged increase in real house prices (RHPG). The econometrically estimated
crisis model for the probability of a crisis (pt) is expressed as the logarithm of
the odds ratio at time t13:
12
The crisis variable takes the value of 1 in a year when any of the following conditions occur: the proportion of non-performing loans to total banking system assets exceeded 10%; the public bailout cost exceeded 2% of GDP; systemic crisis caused large scale bank
nationalisation; extensive bank runs were visible and if not, emergency government intervention was visible.
13
5.1 The results above reflect the scale of importance of each included variable (for developed banking systems).
Variables such as credit growth, inflation and terms of trade are often reported to be significant in studies that include data from less-developed countries. Many studies include these data, due to the relative scarcity of banking crises in developed economies. Thus the samples used reflect highly dissimilar economies. In OP38, these variables dropped out in the model selection process, probably because they use only data from a sample of OECD countries with developed banking systems.
OP38 finds that capital adequacy and liquidity ratios are the main factors explaining banking crisis. A probable explanation is that developed economy banking systems are more likely to be regulated in terms of these variables, and financial regulators will have a mandate to monitor these ratios and implement some corrective action when these indices deteriorate. The OP38 model also includes real house price growth as a significant factor, which is in line with research that links asset price bubbles to banking crises in OECD countries (most notably Reinhart and Rogoff (2008) and (2009)).
5.1 Crisis model improvements
To estimate the benefits of increased prudential standards, the crisis prediction model described above was updated by changing the definition of the liquid asset ratio and ensuring data consistency across the estimation
sample14, and adding a current account variable. We also introduced updated
estimates of the long-term costs of a crisis.15 We discuss each of these
changes below.
5.1.1 Using narrow liquidity
OP38 estimated the impact of liquidity standards on the probability of crisis from data on broad liquid assets (defined as cash and balances with central banks and securities other than shares) for all OECD countries other than the UK, for which comparable data were not available. For the UK, a measure of
‘narrow liquidity’, which comprises cash, gold and government securities, was
used. This divergence in definitions across countries results in an average liquidity ratio for the UK of 5% compared with a range between 15% for France to 24% for the US.
To address this inconsistency, Barrell et al. (2010a) used an alterative data
set. This data is based on a consistent, narrow definition of liquidity (NLIQ) for
all countries in the sample. In these data, the UK’s average liquidity ratio of
5% is closer to other OECD countries’ ratios, which for example are 11% in
the Netherlands and the US. Focusing on narrow liquidity is also more
14
This work was undertaken by NIESR and described in Barrell et al (2010a)
15
The long term economic cost of a crisis is deviation of output from its trend. 3 ) 80 . 2 ( 1 ) 55 . 3 ( 1 ) 58 . 2 (.333 0.118 0.113 0 1 log t t t t t LEV LIQ RHPG p p
appropriate for assessing benefits, as it is more closely aligned with the definition of liquidity used in regulatory standards.
5.1.2 Including the current account
The crisis model from OP38 was also updated to reflect NIESR research (Barrell et al (2010a)) showing that the ratio of the current account balance to
GDP (CBR) plays a significant role in determining the probability of crisis.
Their findings show that as the current account balance improves, the likelihood of crisis decreases. One explanation for this relationship is that inflows of external capital allow banks to engage in excessive lending. This situation, in turn, creates greater risk of the economy overheating, asset price
bubbles and a reduction in lending standards, all of which increase banks’
vulnerability to shocks. To capture this effect, the new crisis prediction model includes a second lag of the UK current account balance. Expressed as the
logarithm of the odds ratio, the modified crisis model can now be written as16:
5.2 As can be seen from the new specification, a higher current account surplus or reduced current account deficit is estimated to reduce the probability of a crisis. Table 5.1 below demonstrates that adding the current account variable results in a significant improvement in model performance relative to the original OP38 model specification.
Table 5.1: Comparison of in-sample performance
Current crisis model OP38 crisis model
Failure to call a real crisis
(Type I error) 25% 35%
False call rate if no crisis
(Type II error) 28% 33%
Source: Barrell et al. (2010a)
The improved crisis model causes our simulations of the benefits of prudential standards in NiGEM to capture some second-order effects of capital and
liquidity ratios on the probability of a crisis. As banks’ costs from higher
prudential standards translate into an increase in margins, internal (UK) demand is reduced, which lowers the current account deficit and results in an additional reduction in the estimated probability of future crises.
5.2 Bayesian probability calculation
As discussed above, our calculation of benefits is based on estimates of the reduction in the probability that a crisis occurs, and the subsequent loss of economic output once a crisis occurs. However, this is not a straightforward calculation between two static economic outcomes. Rather, in a dynamic economic environment, some consideration needs to be given to the impact that the evolution of economic activity has on the likelihood that a crisis
16
t-statistic significance level are shown in parentheses.
2 80 . 2 3 40 . 2 1 30 . 3 1 10 . 4 0.113 0.079 0.236 342 . 0 1 log t t t t t t LEV NLIQ RHPG CBR p p
occurs. We therefore estimate a dynamic path for both the probability of crisis and the loss of output that accompanies a crisis event. Our estimate is expressed in present value terms.
5.2.1 Calculating the probability of crisis
Two significant issues need to be addressed when analysing the impact of changes in prudential policy on the probability of a crisis. First, the probability of crisis in each period changes over the course of the economic cycle. We therefore need to calculate how prudential policy changes the probability of crisis through time. Second, the crisis model estimates the probability of one crisis occurring in a given year but we need to calculate the probability of any number of crises over the economic cycle. We discuss how we approach these issues in turn below.
On the first issue, the crisis model of Section 5.1 estimates the change in crisis probability given the economic and policy environment at a point in time. In particular, the crisis probability will vary over the economic cycle due to changes in real house price growth and the current account balance, even if prudential policy is constant over the cycle. Changes to prudential policy directly affect the crisis probability in a given period but also affect the economy over time, with the full effects not felt until some years after implementation. This generates a profile of the change in probability for each period of time.
For the second issue, we need to calculate the profile of the change in probability given that one or more crises occurs. For each year of the simulation period, the profile calculated from the crisis model provides a binary outcome, i.e. a crisis begins in that year, or it does not. The probability that a crisis occurs over a given period therefore follows a Bernoulli process, in which an exponentially increasing number of events can occur. For example, over a two year period, there are four states of the world to consider: (i) a crisis occurs in the first year, not in the second; (ii) a crisis occurs in the second year, not in the first; (iii) no crisis occurs at all; or (iv) a crisis occurs in both years. Longer time periods require much larger calculations. For example, there are 1,024 potential states of the world over a 10-year period and 32,768 potential states of the world over a 15-year period.
5.2.2 Calculating the benefits of higher prudential standards
While the number of permutations generated by the Bernoulli process is increasingly large as we lengthen the period over which we wish to calculate benefits, the number of calculations needed to make a reasonable estimate of the overall benefits can be reduced substantially. This is because the probability of more than one crisis occurring within any given period is increasingly small as the number of crises rises. We can demonstrate this through a numerical example. If the probability that a crisis occurs in any particular year is reduced from 5% per annum to 4% per annum, we calculate that the reduction in the probability that a single crisis occurs within a 10-year
period is 4 percentage points using the Bernoulli process17. For the event that up to two crises occur within a 10-year period, the reduction in the probability is only six percentage points. The corresponding probability reduction for the event that up to three crises occur over a 10-year period is 6½ percentage points. This shows we can calculate a reasonably accurate measure of the change in the probability using a relatively small number of permutations. Ideally, we would analyse the cost to the economy of multiple banking crises events occurring in quick succession. However, multiple banking crises within a single country have generally not been experienced, so we have no firm estimates of the permanent loss to the economy of such events. For example, Reinhart and Rogoff (2009) look at various types of economic crises (including banking crises) for over two centuries. The evidence they derive suggests that bank crises, although potentially exacerbating crises generated by other means, do not occur in quick succession. This may be because the onset of a banking crisis engenders a response from government that avoids the possibility of another crisis in quick succession.
We have restricted the calculation of benefits to include only the outcomes in which one crisis occurs each year within the period for which we make our calculations. As the probability of having more than one crisis diminishes rapidly and the additional costs to the economy of multiple crises occurring are small, we believe reducing the calculation to include only outcomes with one crisis will capture the great majority of the benefits of any prudential policy package.
5.2.3 Banking crises with permanent and non-permanent costs
As noted above, the crisis model developed in Barrell et al. (2010a) estimates the probability of a banking crisis, regardless of whether this crisis has consequences for the broader economy. If a crisis does not have
consequences for the broader economy, or has ‘non-permanent’ costs, then
the cost of such crises will be very small, or indeed zero, in terms of the loss to GDP. Only crises that impose permanent costs on the economy will therefore be pertinent for calculating the benefits of higher prudential standards. We therefore need to incorporate in the benefits calculation both an estimate of the GDP losses that are likely to occur from a banking crisis with permanent effects, and an estimate of how frequently such crisis are vis-à-vis crises with non-permanent costs.
An estimate of the loss to GDP of crises with permanent effects is based on a detailed literature survey on the depth and length of historical crises, combined with original research carried out by NIESR (Barrell et al (2010c)). Specifically, we calculate the costs of a banking crisis as the cumulative loss in GDP derived from comparing the path of GDP in the absence of a crisis
17
Using a Bernoulli process, the probability that a crisis occurs x times over a period of n
years is given by the following formula:
x nx p p x n x X 1 Pr ,
where p is the probability that a crisis occurs and
! ! ! x n x n x n
with a GDP path that includes post-crisis recession, subsequent recovery but
a permanently lower level of GDP due to a reduction in trend productivity – the
so-called ‘scarring effect of a crisis’ (Barrell and Kirby (2009) and Barrell (2009)). Over the long-term, our estimate shows a permanent reduction in the level of GDP of around 3 per cent compared to a scenario in which a crisis does not occur.
The LEI report (BCBS (2010a)) includes a literature review of the long-term impact of financial crises. According to this analysis, for those crises that have only temporary effects, the improvement in GDP as the economy recovers from the crisis is enough to undo most, if not all, of the losses that occur during the crisis period. Only crises that have permanent effects generate significant, cumulative losses in GDP. Because of this possible pattern of recovery in GDP, many studies find negligible or no cumulative losses. Barrell (2009) found that permanent losses are statistically significant in only one in four crises in developed countries through the period 1980 to 1995.
It seems likely that in future a greater proportion banking crises will be systemic crises, given the increased interconnectedness of the global banking
system and capital mobility18. For our calculation of the benefits we adjust the
ratio from Barrell (2009) so that one in three banking crises leads to a permanent fall in GDP. We discuss in section 7 the impact that different assumptions for this ratio have on our measure of the benefits.
5.3 Alternative formulations of the crisis model
In addition to the changes to the crisis model discussed above, we considered further changes that theoretical, empirical or practical considerations suggested might be important. However, they have not been incorporated in the final version of the model because empirical assessment using the database of 14 OECD countries over the period between 1980 and 2008 showed the effects to be statistically insignificant. Below we describe the further changes considered. Table 5.2 shows the degree to which each of these changes explained the sample data.
5.3.1 Wholesale funding intensity
The ratio of customer deposits to loans (CDLR) is a proxy for funding liquidity
risk as a ratio below one implies each unit of loans is not fully covered by
customer deposits, which are considered to be ‘sticky’ in most circumstances.
So a higher ratio implies that banks are less likely to run out of funding for their lending, whereas a lower ratio suggests a greater reliance on short term wholesale funding, which is considered to be volatile and prone to sudden
withdrawal19. In the run up to a crisis, rapidly expanding loan books may push
banks to a higher than normal reliance on wholesale funding. The first
18
Reinhart and Rogoff (2009) note that there is a correlation between periods of high international capital mobility and banking crises, and argue that financial innovation is a variant of the (capital) liberalisation process. There has been a sharp increase in international capital mobility in recent years, and consequently the proportion of countries involved in banking crises.
19
difference in the ratio of customer deposits to loans is a variable that might reasonably be used to test this hypothesis.
Table 5.2 below shows the results of adding wholesale funding intensity to the original crisis model, through the lagged value of the yearly change in the ratio
of customer deposits to loans (CDLR). This variable has a strong association
with crisis prediction and it was a successful addition to the model, also